In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.

Example-based single image super-resolution (SR) has recently shown outcomes with high reconstruction performance. Several methods based on neural networks have successfully introduced techniques into SR problem. In this paper, we propose a three-dimensional (3D) convolutional neural network to generate high-resolution (HR) brain image from its input low-resolution (LR) with the help of patches of other HR brain images. Our work demonstrates the need of fitting data and network parameters for 3D brain MRI.

Data assimilation is a key component of operational systems and scientific studies for the understanding, modeling, forecasting and reconstruction of earth systems informed by observation data. Here, we investigate how physics‐informed deep learning may provide new means to revisit data assimilation problems. We develop a so‐called end‐to‐end learning approach, which explicitly relies on a variational data assimilation formulation. Using automatic differentiation embedded in deep learning framework, the key novelty of the proposed physics‐informed approach is to allow the joint training of the representation of the dynamical process of interest as well as of the solver of the data assimilation problem. We may perform this joint training using both supervised and unsupervised strategies. Our numerical experiments on Lorenz‐63 and Lorenz‐96 systems report significant gain w.r.t. a classic gradient‐based minimization of the variational cost both in terms of reconstruction performance and optimization complexity. Intriguingly, we also show that the variational models issued from the true Lorenz‐63 and Lorenz‐96 ODE representations may not lead to the best reconstruction performance. We believe these results may open new research avenues for the specification of assimilation models for earth systems, both to speed‐up the inversion problem with trainable solvers but possibly more importantly in the way data assimilation systems are designed, for instance regarding the representation of geophysical dynamics.

Representing maritime traffic patterns and detecting anomalies from them are key to vessel monitoring and maritime situational awareness. We propose a novel approach—referred to as GeoTrackNet —for maritime anomaly detection from AIS data streams. Our model exploits state-of-the-art neural network schemes to learn a probabilistic representation of AIS tracks and a contrario detection to detect abnormal events. The neural network provides a new means to capture complex and heterogeneous patterns in vessels’ behaviours, while the a contrario detector takes into account the fact that the learnt distribution may be location-dependent. Experiments on a real AIS dataset comprising more than 4.2 million AIS messages demonstrate the relevance of the proposed method compared with state-of-the-art schemes.

Vessel trajectory prediction plays a pivotal role in numerous maritime applications and services. While the Automatic Identification System (AIS) offers a rich source of information to address this task, forecasting vessel trajectory using AIS data remains challenging, even for modern machine learning techniques, because of the inherent heterogeneous and multimodal nature of motion data. In this paper, we propose a novel approach to tackle these challenges. We introduce a discrete, high-dimensional representation of AIS data and a new loss function designed to explicitly address heterogeneity and multimodality. The proposed model—referred to as TrAISformer —is a modified transformer network that extracts long-term temporal patterns in AIS vessel trajectories in the proposed enriched space to forecast the positions of vessels several hours ahead. We report experimental results on real, publicly available AIS data. TrAISformer significantly outperforms state-of-the-art methods, with an average prediction performance below 10 nautical miles up to ~10 hours.